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168 Chapter 4 400 350 300 250 200 150 100 50 0 0.76 0.78 Fig. 4-37. Discharge loss versus mass utilization efficiency for our microwave thruster example with perfect radial confinement. L = 10 cm L = 20 cm L = 40 cm 0.80 0.82 0.84 Mass Utilization Efficiency 0.86 0.88 0.90 0.92 0.94 0.96 and reduces the axial losses. Because the magnetic moment (defined as mv2/2B) is invariant along the field lines, electrons with sufficient initial perpendicular velocity are reflected from the increasing magnetic field as their parallel energy is converted into rotational energy. The electrons that are lost have a parallel velocity of v||>v Rm 1, (4.6-34) where Rm is the mirror ratio given by Bmax / Bm . For example, if the mirror ratio is 5, only electrons with a parallel velocity twice that of their perpendicular velocity will be lost. If the electrons have a Maxwellian distribution with a temperature Te , then the number of particles with v|| > 2v is e–2 =13.5%, so a large majority of the population is reflected. Since the cyclotron heating adds perpendicular energy to the electrons, mirror ratios of 4 to 6 are very efficient in confining the heated electrons that produce ionization. The ion source shown in Fig. 4-36 utilizes electromagnets to produce the high field over a significant volume and also to create the confining mirror ratio. However, the power required to operate the electromagnets in this design increases the effective discharge loss and limits the electrical efficiency of the device in thruster applications. In addition, it is difficult to create large area Discharge Loss (eV/ion)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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